A two-stage nested sampling design was used to collect data to estimate the mean porosity of paper emerging from a paper machine. Ten patches of paper were randomly selected from the end of the paper roll, and four porosity readings were made on each. The data are shown in the following table.

a. Perform an analysis of variance on the data. Give the ANOVA summary table.

b. Obtain the estimates of σ_α² = 0 and σ².

c. Do the data provide sufficient evidence to indicate that the variation in porosity between patches exceeds the variation of porosity within patches? Test using α = .05.

PAPER Paper Patch Porosity Readings 974 978 976 975 2 981 985 978 986 3 1,014 1,012 1,018 1,010 4 990 996 989 988 5 1,012 1,009 1,011 1,012 6. 978 980 974 982 7 988 979 986 983 8 1,004 1,001 1,008 1,008 9. 989 984 982 983 10 999 1,002 998 1,003